engMax Planck Institute for Gravitational Physics (Albert Einstein Institute)Living Reviews in Relativity1433-83511998-01-261210.12942/lrr-1998-2lrr-1998-2articlePhysical and Relativistic Numerical CosmologyPeter Anninos1University of California, Lawrence Livermore National LaboratoryIn order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes within them. A sample of numerical calculations addressing specific issues in cosmology are reviewed in this article: from the Big Bang singularity dynamics to the fundamental interactions of gravitational waves; from the quark--hadron phase transition to the large scale structure of the Universe. The emphasis, although not exclusively, is on those calculations designed to test different models of cosmology against the observed Universe.http://www.livingreviews.org/lrr-1998-2